Detecting Three-Dimensional Associations in Large Data Set

The associations detection among variables in the large dataset is recently important due to the rapid growth rate of data. The interested associations can provide references for solving the problems such as dimension reduction and feature selection. Many methods have done on the associations detection of pairwise variables. The multi-dimensional variables, especially three-dimensional variables, is rarely studied. The relationships among them cannot be revealed by the detection of pairwise variables methods. A new method of Maximal three-dimensional information coefficient (MTDIC) is proposed which is able to indicate the associations of three-dimensional variables. The correlation coefficient is calculated from the three-dimensional mutual information. The World Health Organization (WHO) data and the Tara data are selected to evaluate their associations. The experiment is verified by comparing the coefficient results with the Distance correlation (Dcor). The accurate association strength is obtained by an iterative optimization procedure on sorting descending order of coefficients. The MTDIC performs better than the Dcor in generality and equitability properties.